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A058560 McKay-Thompson series of class 20e for Monster. 1

%I #19 Jul 03 2018 03:57:48

%S 1,2,-1,0,3,0,3,-4,0,2,3,8,-4,0,9,4,12,-10,0,8,10,26,-14,0,23,10,35,

%T -28,0,26,26,64,-39,0,57,28,89,-66,0,64,56,150,-91,0,125,66,202,-148,

%U 0,148,120,320,-198,0,259,144,429,-302,0,312,243,648,-405,0,511,292,860,-600,0,622

%N McKay-Thompson series of class 20e for Monster.

%H G. C. Greubel, <a href="/A058560/b058560.txt">Table of n, a(n) for n = -1..1000</a>

%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Comm. Algebra 22, No. 13, 5175-5193 (1994).

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F Expansion of (T10b + 4)^(1/2), where T10b = A058103, in powers of q. - _G. C. Greubel_, Jun 21 2018

%e T20e = 1/q + 2*q - q^3 + 3*q^7 + 3*q^11 - 4*q^13 + 2*q^17 + 3*q^19 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A:= eta[q]/eta[q^25]; B:= (eta[q^2]*eta[q^25])/(eta[q]*eta[q^50]); c := ((eta[q]*eta[q^2])/( eta[q^5]*eta[q^10]))^2; d:= ((eta[q^5]*eta[q^10])/( eta[q^25]*eta[q^50]) )^2; T10b := (2 + c + 5*(c/(A)^2)*(1 - 1/B)^2 + 25/d); a:= CoefficientList[Series[(q*(T10b + 4) + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* _G. C. Greubel_, Jun 21 2018, fixed by _Vaclav Kotesovec_, Jul 03 2018 *)

%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

%K sign

%O -1,2

%A _N. J. A. Sloane_, Nov 27 2000

%E Terms a(12) onward added by _G. C. Greubel_, Jun 21 2018

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Last modified March 28 14:02 EDT 2024. Contains 371254 sequences. (Running on oeis4.)